## Word problems based on formulation of linear programming, Operation Research

Assignment Help:

Word problems based on formulation of linear programming problems.

2.   A manufacturer produces nuts and bolts for industrial machinery. It takes 1 hour of work on machine 1 and 3 hours of work on machine 2 to produce a package of nuts. It takes 3 hours on machine 1 and 1 hour on machine 2 to produce a package of bolts. He earns a profit of Rs. 2.50 per package on nuts and Rs. 1 per package on bolts. Form a LPP to maximize his profit, if he operates each machine for almost 12 hours.

 script solution Let x packages of nuts and y packages of bolts be produced. The objective of the manufacturer to maximize the profit is Total Time required on machine 1 to produce x packages of nuts and y packages of bolts is equal to   Total Time required on the machine 2 to produce x packages of nuts and y packages of bolts is equal to  s According to restrictions, For machine 1 For machine 2   Maximize z is equal to   Subject to constraints     To solve this graphically, let us take The lines are drawn using suitable points on the graph. The lines intersect at P(3,3) Now shade the region of intersection of the lines. The feasible region is OAPB For the corner point O(0,0), z= For the corner point A(4,0) For the corner point P(3,3,) For the corner point B(0,4) Clearly z is maximum at x=3 , y=3 and the maximum value is 10.50 2.50x + 1y     1x + 3y     3x + 1y           X + 3y ≤ 12 3x + y ≤ 12 and x,y≥0   2.50x + y   X + 3y ≤ 12 3x + y ≤ 12 X ≥ 0, y ≥ 0 X + 3y =12 3x + y = 12, x=0, y=0           O(0,0),A(4,0),P(3,3,),B(0,4) 2.5(0) +1(0)=0 2.5(4)+1(0)=10 2.5(3)+1(3)=10.5 2.5(0)+1(4)=4

3.   A shopkeeper deals in 2 items → wall hangings and artificial plants. He had a space to store 80 pieces and Rs. 15000 to invest. A wall hangings cost him Rs. 300 and artificial plant Rs. 150. He can sell a wall hanging at a profit of Rs. 50 and artificial plant at a profit of Rs. 18. Assuming that he can sell all the items that he buys, formulate a LPP in order to maximize his profit.\

 script solution Let x be the number of wall hangings and y be the number of artificial plants. Profit of dealer is equal to Objective function z is equal to Since dealer invest atmost Rs. 15000 Therefore Or Also a dealer has space to store atmost 80 pieces. Therefore,   Maximize z is equal to Subject to constraints       To solve this graphically, we need to draw the graph Let us the draw the lines 2x + y ≤100 X + y ≤ 80 X ≥ 0, y ≥ 0 On the graph by using suitable points. The points of intersection are Then shade the region of intersection of these two lines The feasible points are OABC Now to obtain the maximum value; For The corner point O(0,0), z= For the corner point A(50,0) For the corner point B(20,60) For the corner point C(0,100) Clearly we get the maximum value of 2500 at A.(50,0) 50x + 18y 50x + 18y     300x + 150y ≤ 15000 2x + y ≤ 100     X + y ≤ 80 X ≥ 0, y ≥ 0 Z = 50x + 18y 2x + y ≤100 X + y ≤ 80 X ≥ 0, y ≥ 0                   (20,60)     O(0,0),A(50,0),B(20,60),(C(0,100)       50(0)+18(0)=0   50(50)+18(0)=2500 50(20)+18(60)=2080 50(0)+18(100)=1800

#### Software, role of computer software in operation research

role of computer software in operation research

#### T, #Principles of OR

#Principles of OR

#### Survey method, This method involves a systematic and comprehensive study...

This method involves a systematic and comprehensive study of a particular community organization group etc, with a view to the analysis of a social problem and the presen

#### Linear programming , #questionQuestion. a paper mill produces two grades o...

#questionQuestion. a paper mill produces two grades of paper viz.,xand y.Bacause of raw material restrictions, it cannot produce more than 400 tones of grade x paper and 300 tons

#### Chi square test as a test of homogeneit, Chi Square Test as a Test of Homog...

Chi Square Test as a Test of Homogeneit The X 2 test of homogeneity is an  extension of the chi square  test of independence of attributes. It is  designed to determine  whet

#### Non-governmental organisation, Name the feature which is not normally assoc...

Name the feature which is not normally associated with a Non-Governmental Organisation (NGO)?  Government funded is the organisation.

#### Rank sum test the mann whitney u - test, RANK SUM TEST THE  MANN WHITNEY U...

RANK SUM TEST THE  MANN WHITNEY U - TEST Mann  Whitney u test is an alternative to the  samples  test. This  test is based  on the ranks  of the  observation of two samples pu

#### Sequencing problem, how do you use gantt chart for solving sequencing probl...

how do you use gantt chart for solving sequencing problem ? why is it not employed for solving larger problems?

#### Optimization , A company uses 4 pounds of resource 1 to make each unit of X...

A company uses 4 pounds of resource 1 to make each unit of X1 and 3 pounds of resource 1 to make each unit of X2. There are only 150 pounds of resource 1 available. Which of the fo

#### Construction procedure for research tool, CONSTRUCTION PROCEDURE The c...

CONSTRUCTION PROCEDURE The construction of an interview schedule or questionnaire is a time consuming task requiring considerable attention to all the details. The investig  